Mechanisms for attenuation in cancellous-bone-mimicking phantoms

What kind of waves are measured in trabecular bone?

The paper discusses the fundamental mechanisms underlying the interaction between ultrasound and trabecular bone, which is considered a two-phase material. When fluid-saturated cancellous bone is interrogated by ultrasound, in some cases, one or two wave modes are observed. Many authors claim that these waves correspond to the fast and slow waves predicted by Biot's theory of elastic wave propagation in fluid-saturated porous media. Within our analysis of the physical conditions, predictions of the existing two-phase models of the propagation of ultrasonic waves in the material as well as numerical simulations for fluid-saturated trabecular bone were performed. On the basis of the theoretical results (from numerical studies) and arguments presented in this paper, we aimed to answer the question of whether two waves observed in ultrasonic wave transmission studies can be interpreted as the fast and slow waves predicted by Biot's theory.

Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements From Arrays-Part I: Theory and Impact on Diagnostic Safety Indexes

This article reports underestimation of mechanical index (MI) and nonscanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after ten weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly focused beams and nonlinear, nonscanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner/transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015 to 2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse filter suggests that maximally achievable values for MI, TIB, thermal dose ( t ₄₃ ), and spatial-peak-temporal-average intensity ( [Formula: see text]) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI t ₄₃ ), 43% ± 39% (ARFI [Formula: see text]), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler t ₄₃ ), and 33% ± 27% (pulsed Doppler [Formula: see text]). These values correspond to frequencies of 3.2 ± 1.3 (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves the accuracy of estimates of MI, TIB, t ₄₃ , and [Formula: see text] for ARFI and pulsed Doppler signals.

Evaluation of Structural Anisotropy in a Porous Titanium Medium Mimicking Trabecular Bone Structure Using Mode-Converted Ultrasonic Scattering

The mode-converted (longitudinal to transverse, L-T) ultrasonic scattering method was utilized to characterize the structural anisotropy of a phantom mimicking the structural properties of trabecular bone. The sample was fabricated using metal additive manufacturing from high-resolution computed tomography (CT) images of a sample of trabecular horse bone with strong anisotropy. Two focused transducers were used to perform the L-T ultrasonic measurements. A normal incidence transducer was used to transmit longitudinal ultrasonic waves into the sample, while the scattered transverse signals were received by an oblique incidence transducer. At multiple locations on the sample, four L-T measurements were performed by collecting ultrasonic scattering from four directions. The amplitude of the root mean square (rms) of the collected ultrasonic scattering signals was calculated for each L-T measurement. The ratios of rms amplitudes for L-T measurements in different directions were calculated to characterize the anisotropy of sample. The results show that the amplitude of L-T converted scattering is highly dependent on the direction of microstructural anisotropy. A strong anisotropy of the microstructure was observed, which coincides with simulation results previously published on the same structure as well as with the anisotropy estimated from the CT images. These results suggest the potential of mode-converted ultrasonic scattering methods to assess the anisotropy of materials with porous, complex structures, including trabecular bone.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Ultrasound tomography in bone mimicking phantoms: Simulations and experiments

Bone quality assessment for osteoporosis diagnosis is usually performed using dual energy X-ray absorptiometry or X-ray quantitative computed tomography. Recent research demonstrated that both methods are inaccurate in diagnosing osteoporosis since they rely only on the bone mineral density. The literature on bone quantitative ultrasound suggests that ultrasonic waves are sensitive to multiple significant bone parameters such as mechanical properties, the bone volume fraction, and the micro-architecture. Typical ultrasound tomography techniques are limited to image objects with a low speed of sound contrast relative to a background medium. In this study, the possibility of adapting a more advanced ultrasound inversion technique referred to as the hybrid algorithm for robust breast ultrasound tomography for velocity mapping of bone mimicking phantoms was examined. The cortical bone thickness and the cortical bone speed of sound, which are directly related to the bone elastic properties, are parameters strongly correlated with the overall bone quality. A finite element model and an experimental test bench were developed to adapt the hybrid algorithm for robust breast ultrasound tomography to bone quality assessment. Although artefacts were present in the images generated, the results obtained enabled discrimination of a healthy bone phantom over an osteoporotic bone phantom based on the cortical bone thickness and the average cortical bone velocity. The speed of sound inside the cortical region of the bone phantoms was underestimated by 9.38% for the osteoporotic phantom, and by 10.68% for the healthy phantom relative to the values supplied by the bone phantom manufacturer, but there was a difference of 3.97% between the two samples. The difference between the measured cortical bone thickness of the reconstructed image and the X-ray computed tomography images was on average 0.4 mm.

Characterization of a polymer, open-cell rigid foam that simulates the ultrasonic properties of cancellous bone

Materials that simulate the ultrasonic properties of tissues are used widely for clinical and research purposes. However, relatively few materials are known to simulate the ultrasonic properties of cancellous bone. The goal of the present study was to investigate the suitability of using a polymer, open-cell rigid foam (OCRF) produced by Sawbones^®. Measurements were performed on OCRF specimens with four different densities. Ultrasonic speed of sound and normalized broadband ultrasonic attenuation were measured with a 0.5 MHz transducer. Three backscatter parameters were measured with a 5 MHz transducer: apparent integrated backscatter, frequency slope of apparent backscatter, and normalized mean of the backscatter difference. X-ray micro-computed tomography was used to measure the microstructural characteristics of the OCRF specimens. The trabecular thickness and relative bone volume of the OCRF specimens were similar to those of human cancellous bone, but the trabecular separation was greater. In most cases, the ultrasonic properties of the OCRF specimens were similar to values reported in the literature for cancellous bone, including dependence on density. In addition, the OCRF specimens exhibited an ultrasonic anisotropy similar to that reported for cancellous bone.

Novel Cranial Implants of Yttria-Stabilized Zirconia as Acoustic Windows for Ultrasonic Brain Therapy

Therapeutic ultrasound can induce changes in tissues by means of thermal and nonthermal effects. It is proposed for treatment of some brain pathologies such as Alzheimer's, Parkinson's, Huntington's diseases, and cancer. However, cranium highly absorbs ultrasound reducing transmission efficiency. There are clinical applications of transcranial focused ultrasound and implantable ultrasound transducers proposed to address this problem. In this paper, biocompatible materials are proposed for replacing part of the cranium (cranial implants) based on low porosity polycrystalline 8 mol% yttria-stabilized-zirconia (8YSZ) ceramics as acoustic windows for brain therapy. In order to assess the viability of 8YSZ implants to effectively transmit ultrasound, various 8YSZ ceramics with different porosity are tested; their acoustic properties are measured; and the results are validated using finite element models simulating wave propagation to brain tissue through 8YSZ windows. The ultrasound attenuation is found to be linearly dependent on ceramics' porosity. Results for the nearly pore-free case indicate that 8YSZ is highly effective in transmitting ultrasound, with overall maximum transmission efficiency of ≈81%, compared to near total absorption of cranial bone. These results suggest that 8YSZ polycrystals could be suitable acoustic windows for ultrasound brain therapy at 1 MHz.

Solid volume fraction estimation of bone:marrow replica models using ultrasound transit time spectroscopy

The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.

Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms

In this paper, ultrasound measurements of 1:1 scale three-dimensional (3D) printed trabecular bone phantoms are reported. The micro-structure of a trabecular horse bone sample was obtained via synchrotron x-ray microtomography, converted to a 3D binary data set, and successfully 3D-printed at scale 1:1. Ultrasound through-transmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing. As in real anisotropic trabecular bone, both the fast and slow waves were observed. This illustrates the potential of stereolithography and the relevance of such bone phantoms for the study of ultrasound propagation in bone.

Dependences of quantitative ultrasound parameters on frequency and porosity in water-saturated nickel foams

The frequency-dependent phase velocity, attenuation coefficient, and backscatter coefficient were measured from 0.8 to 1.2 MHz in 24 water-saturated nickel foams as trabecular-bone-mimicking phantoms. The power law fits to the measurements showed that the phase velocity, the attenuation coefficient, and the backscatter coefficient were proportional to the frequency with exponents n of 0.95, 1.29, and 3.18, respectively. A significant linear correlation was found between the phase velocity at 1.0 MHz and the porosity. In contrast, the best regressions for the normalized broadband ultrasound attenuation and the backscatter coefficient at 1.0 MHz were obtained with the polynomial fits of second order.

Frequency specific ultrasound attenuation is sensitive to trabecular bone structure

This study investigated the efficacy of frequency modulated ultrasound attenuation in the assessment of the trabecular structural properties. Four frequency modulated signals were created to represent four frequency bands centered at 500 kHz, 900 kHz, 1.3 MHz and 1.7 MHz with the bandwidth of 400 kHz. Five 1-cm trabecular cubes were harvested from fresh bovine distal femur. The cubes underwent four steps of demineralization process to expand the sample size to 25 with the greater variations of the structural properties for the better correlation study. Pearson correlation study was performed between the ultrasound attenuation in four frequency bands and the trabecular structural properties. The results showed that correlations of frequency modulated ultrasound attenuation to the trabecular structural properties are dependent on frequency bands. The attenuation in proximal-distal orientation had the highest correlation to BV/TV (R(2) = 0.73, p < 0.001) and trabecular thickness (R(2) = 0.50, p < 0.001) at the frequency band centered at 1.7 MHz. It was equivalent in the four frequency bands in correlation to the trabecular number (average R(2) = 0.80, p < 0.001) and to the trabecular separation (average R(2) = 0.83, p < 0.001). The attenuation in anterio-posterial orientation had the highest correlation to BV/TV (R(2) = 0.80, p < 0.001) and trabecular thickness (R(2) = 0.71, p < 0.001) at the frequency band centered at 1.3 MHz. The attenuation in the first frequency band was the most sensitive to the trabecular number (R(2) = 0.71, p < 0.001) and trabecular separation (R(2) = 0.80, p < 0.001). No significant correlation was observed for the attenuation in medial-lateral orientation across the four frequency bands.

Investigation of the influence of reflection on the attenuation of cancellous bone

The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin 'transient' layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection. The proposed representative volume element together with the multiscale finite element is used to simulate the wave propagation and to evaluate the attenuation coefficient for samples with different effective densities in the dependence of the applied excitation frequency. The obtained numerical values show a very good agreement with the experimental results. Moreover, the model enables the determination of the upper and the lower bound for the attenuation coefficient.

Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz

The frequency-dependent attenuation and backscatter coefficients were measured in 25 bovine femoral trabecular bone samples from 0.2 to 1.2 MHz. When the average attenuation coefficient was fitted to a nonlinear power law α(f)=α(0)+α(1)f(n), the exponent n was found to be 1.65. In contrast, the average backscatter coefficient was fitted to a power law η(f)=η(1)f(n) and the exponent n was measured as 3.25. The apparent bone density was significantly correlated with the parameter α(1) (0.2-0.7 MHz: r = 0.852, 0.6-1.2 MHz: r = 0.832) as well as the backscatter coefficient (0.5 MHz: r = 0.751, 1.0 MHz: r = 0.808).

Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz

The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.